Contents
cgeev - compute for an N-by-N complex nonsymmetric matrix A,
the eigenvalues and, optionally, the left and/or right
eigenvectors
SUBROUTINE CGEEV(JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBVL, JOBVR
COMPLEX A(LDA,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER N, LDA, LDVL, LDVR, LDWORK, INFO
REAL WORK2(*)
SUBROUTINE CGEEV_64(JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBVL, JOBVR
COMPLEX A(LDA,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
INTEGER*8 N, LDA, LDVL, LDVR, LDWORK, INFO
REAL WORK2(*)
F95 INTERFACE
SUBROUTINE GEEV(JOBVL, JOBVR, [N], A, [LDA], W, VL, [LDVL], VR, [LDVR],
[WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, VL, VR
INTEGER :: N, LDA, LDVL, LDVR, LDWORK, INFO
REAL, DIMENSION(:) :: WORK2
SUBROUTINE GEEV_64(JOBVL, JOBVR, [N], A, [LDA], W, VL, [LDVL], VR,
[LDVR], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBVL, JOBVR
COMPLEX, DIMENSION(:) :: W, WORK
COMPLEX, DIMENSION(:,:) :: A, VL, VR
INTEGER(8) :: N, LDA, LDVL, LDVR, LDWORK, INFO
REAL, DIMENSION(:) :: WORK2
C INTERFACE
#include <sunperf.h>
void cgeev(char jobvl, char jobvr, int n, complex *a, int
lda, complex *w, complex *vl, int ldvl, complex
*vr, int ldvr, int *info);
void cgeev_64(char jobvl, char jobvr, long n, complex *a,
long lda, complex *w, complex *vl, long ldvl, com-
plex *vr, long ldvr, long *info);
cgeev computes for an N-by-N complex nonsymmetric matrix A,
the eigenvalues and, optionally, the left and/or right
eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean
norm equal to 1 and largest component real.
JOBVL (input)
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input)
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) The order of the matrix A. N >= 0.
A (input/output)
On entry, the N-by-N matrix A. On exit, A has
been overwritten.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
W (output)
W contains the computed eigenvalues.
VL (input)
If JOBVL = 'V', the left eigenvectors u(j) are
stored one after another in the columns of VL, in
the same order as their eigenvalues. If JOBVL =
'N', VL is not referenced. u(j) = VL(:,j), the
j-th column of VL.
LDVL (input)
The leading dimension of the array VL. LDVL >= 1;
if JOBVL = 'V', LDVL >= N.
VR (input)
If JOBVR = 'V', the right eigenvectors v(j) are
stored one after another in the columns of VR, in
the same order as their eigenvalues. If JOBVR =
'N', VR is not referenced. v(j) = VR(:,j), the
j-th column of VR.
LDVR (input)
The leading dimension of the array VR. LDVR >= 1;
if JOBVR = 'V', LDVR >= N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >=
max(1,2*N). For good performance, LDWORK must
generally be larger.
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
> 0: if INFO = i, the QR algorithm failed to com-
pute all the eigenvalues, and no eigenvectors have
been computed; elements and i+1:N of W contain
eigenvalues which have converged.